Type II supernovae (SNe) often exhibit a linear polarization, arising from free-electron scattering, with complicated optical signatures, both in the continuum and in lines. Focusing on the early nebular phase, at a SN age of 200d, we conduct a systematic study of the polarization signatures associated with a 56Ni `blob that breaks spherical symmetry. Our ansatz, supported by nonLTE radiative transfer calculations, is that the primary role of such a 56Ni blob is to boost the local density of free electrons, which is otherwise reduced following recombination in SNe II. Using 2D polarized radiation transfer modeling, we explore the influence of such an electron-density enhancement, varying its magnitude N_e_fac, its velocity location V_blob, and its spatial extent. For plausible N_e_fac values of a few tens, a high-velocity blob can deliver a continuum polarization P_cont of 0.5-1.0% at 200d. Our simulations reproduce the analytic scalings for P_cont, and in particular the linear growth with the blob radial optical depth. The most constraining information is, however, carried by polarized line photons. For a high V_blob, the polarized spectrum appears as a replica of the full spectrum, scaled down by a factor 100 to 1000 (i.e., 1/P_cont), and redshifted by an amount V_blob(1-cos(alpha_los)), where alpha_los is the line of sight angle. As V_blob is reduced, the redshift decreases and the replication deteriorates. Lines whose formation region overlap with the blob appear weaker and narrower in the polarized flux. Because of its dependence on inclination (~ sin^2 alpha_los), the polarization preferentially reveals asymmetries in the plane perpendicular to the line of sight. With the adequate choice of electron-density enhancement, some of these results may apply to asymmetric explosions in general, or to the polarization signatures from newly-formed dust in the outer ejecta. [abridged]
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